Search Results (664)

For a significant fluid model and the truncated M-fractional (1 + 1)-dimensional nonlinear generalized water wave equation, distinct types of truncated M-fractional wave solitons are obtained. Ocean waves, tidal waves, weather simulations, river and irrigation flows, tsunami predictions, and more are all explained by this model. We use the improved $(G^{\prime }/G)$ expansion technique and a modified extended direct algebraic technique to obtain these solutions. Results for trigonometry, hyperbolic, and rational functions are obtained. The impact of the fractional-order derivative is also covered. We use Mathematica software to verify our findings. Furthermore, we use contour graphs in two and three dimensions to illustrate some wave solitons that are obtained. The results obtained have applications in ocean engineering, fluid dynamics, and other fields. The stability analysis of the considered equation is also performed. Moreover, the stationary solutions of the concerning equation are studied through modulation instability. Furthermore, the used methods are useful for other nonlinear fractional partial differential equations in different areas of applied science and engineering. Full article

The current study demonstrates the buckling properties of composite laminates reinforced with MWCNT fillers using a novel higher-order shear and normal deformation theory (HSNDT), which considers the effect of thickness in its mathematical formulation. The hybrid HSNDT combines polynomial and hyperbolic functions that ensure the parabolic shear stress profile and zero shear stress boundary condition at the upper and lower surface of the plate, hence removing the need for a shear correction factor. The plate is made up of carbon fiber bounded together with polymer resin matrix reinforced with MWCNT fibers. The mechanical properties are homogenized by a Halpin–Tsai scheme. The MATLAB R2019a code was developed in-house for a finite element model using C⁰ continuity nine-node Lagrangian isoparametric shape functions. The geometric nonlinear and linear stiffness matrices are derived using the principle of virtual work. The solution of the eigenvalue problem enables estimation of the critical buckling loads. A convergence study was carried out and model efficiency was corroborated with the existing literature. The model contains only seven degrees of freedom, which significantly reduces computation time, facilitating the comprehensive parametric studies for the buckling stability of the plate. Full article

The objective of the present study is to detect chirped optical solitons of the perturbed Chen–Lee–Liu equation with full nonlinearity. By virtue of the traveling wave hypothesis, the discussed model is reduced to a simple form known as an elliptic equation. The latter equation, which is a second-order ordinary differential equation, is handled by the undetermined coefficient method of two forms expressed in terms of the hyperbolic secant and tangent functions. Additionally, the auxiliary equation method is applied to derive several miscellaneous solutions. Various types of chirped solitons are revealed such as W-shaped, bright, dark, gray, kink and anti-kink waves. Taking into consideration the existence conditions, the dynamical behaviors of optical solitons and their corresponding chirp are illustrated. The modulation instability of the perturbed CLL equation is examined by means of the linear stability analysis. It is found that all solutions are stable against small perturbations. These entirely new results, compared to previous works, can be employed to understand pulse propagation in optical fiber mediums and dynamic characteristics of waves in plasma. Full article

This study presents a theoretical model for the thermoelastic response in transmission-mode photoacoustic systems that feature a two-layer structure. The model incorporates volumetric optical absorption in both layers and is based on classical heat conduction theory, hyperbolic generalized heat conduction theory, and fractional heat conduction models including inertial memory in Generalizations of the Cattaneo Equation (GCEI, GCEII, and GCEIII). To validate the model, comparisons were made with the existing literature models. Using the proposed model, the thermoelastic photoacoustic response of a two-layer system composed of a 3D-printed porous polyamide (PA12) substrate coated with a thin, highly absorptive protective dye layer is analyzed. We obtain that the thickness and thermal conduction in properties of the coating are very important in influencing the thermoelastic component and should not be overlooked. Furthermore, the thermoelastic component is affected by the selected fractional model—whether it is subdiffusion or superdiffusion—along with the value of the order of the fractional derivative, as well as the optical absorption coefficient of the layer being investigated. Additionally, it is concluded that the phase has a greater impact than the amplitude when selecting the appropriate theoretical heat conduction model. Full article

Accurate settlement prediction for high-speed railway (HSR) soft foundations remains challenging due to the irregular and dynamic nature of real-world monitoring data, often represented as non-equidistant and non-stationary time series (NENSTS). Existing empirical models lack clear applicability criteria under such conditions, resulting in subjective model selection. This study introduces a Monte Carlo-based evaluation framework that integrates data-driven simulation with geotechnical principles, embedding the concept of symmetry across both modeling and assessment stages. Equivalent permeability coefficients (EPCs) are used to normalize soil consolidation behavior, enabling the generation of a large, statistically robust dataset. Four empirical settlement prediction models—Hyperbolic, Exponential, Asaoka, and Hoshino—are systematically analyzed for sensitivity to temporal features and resistance to stochastic noise. A symmetry-aware comprehensive evaluation index (CEI), constructed via a robust entropy weight method (REWM), balances multiple performance metrics to ensure objective comparison. Results reveal that while settlement behavior evolves asymmetrically with respect to EPCs over time, a symmetrical structure emerges in model suitability across distinct EPC intervals: the Asaoka method performs best under low-permeability conditions (EPC ≤ 0.03 m/d), Hoshino excels in intermediate ranges (0.03 < EPC ≤ 0.7 m/d), and the Exponential model dominates in highly permeable soils (EPC > 0.7 m/d). This framework not only quantifies model robustness under complex data conditions but also formalizes the notion of symmetrical applicability, offering a structured path toward intelligent, adaptive settlement prediction in HSR subgrade engineering. Full article

This manuscript aims to explore localized waves for the nonlinear partial differential equation referred to as the $(1+1)$-dimensional generalized Kundu–Eckhaus equation with an additional dispersion term that describes the propagation of the ultra-short femtosecond pulses in an optical fiber. This research delves deep into the characteristics, behaviors, and localized waves of the $(1+1)$-dimensional generalized Kundu–Eckhaus equation. We utilize the multivariate generalized exponential rational integral function method (MGERIFM) to derive localized waves, examining their properties, including propagation behaviors and interactions. Motivated by the generalized exponential rational integral function method, it proves to be a powerful tool for finding solutions involving the exponential, trigonometric, and hyperbolic functions. The solutions we found using the MGERIF method have important applications in different scientific domains, including nonlinear optics, plasma physics, fluid dynamics, mathematical physics, and condensed matter physics. We apply the three-dimensional (3D) and contour plots to illuminate the physical significance of the derived solution, exploring the various parameter choices. The proposed approaches are significant and applicable to various nonlinear evolutionary equations used to model nonlinear physical systems in the field of nonlinear sciences. Full article

In this study, we investigate the fractional Tzitzéica equation, a nonlinear evolution equation known for modeling complex phenomena in various scientific domains such as solid-state physics, crystal dislocation, electromagnetic waves, chemical kinetics, quantum field theory, and nonlinear optics. Using the (G′/G, 1/G)-expansion approach, we derive different categories of exact solutions, like hyperbolic, trigonometric, and rational functions. The beta fractional derivative is used here to generalize the classical idea of the derivative, which preserves important principles. The derived solutions with broader nonlinear wave structures are periodic waves, breathers, peakons, W-shaped solitons, and singular solitons, which enhance our understanding of nonlinear wave dynamics. In relation to these results, the findings are described by showing the solitons’ physical behaviors, their stabilities, and dispersions under fractional parameters in the form of contour plots and 2D and 3D graphs. Comparisons with earlier studies underscore the originality and consistency of the (G′/G, 1/G)-expansion approach in addressing fractional-order evolution equations. It contributes new solutions to analytical problems of fractional nonlinear integrable systems and helps understand the systems’ dynamic behavior in a wider scope of applications. Full article

This paper investigates an integrable spin system known as the Myrzakulov-XIII (M-XIII) equation through geometric and gauge-theoretic methods. The M-XIII equation, which describes dispersionless dynamics with curvature-induced interactions, is shown to admit a geometric interpretation via curve flows in three-dimensional space. We establish its gauge equivalence with the complex coupled dispersionless (CCD) system and construct the corresponding Lax pair. Using the Sym–Tafel formula, we derive exact soliton surfaces associated with the integrable evolution of curves and surfaces. A key focus is placed on the role of geometric and gauge symmetry in the integrability structure and solution construction. The main contributions of this work include: (i) a commutative diagram illustrating the connections between the M-XIII, CCD, and surface deformation models; (ii) the derivation of new exact solutions for a fractional extension of the M-XIII equation using the Kudryashov method; and (iii) the classification of these solutions into trigonometric, hyperbolic, and exponential types. These findings deepen the interplay between symmetry, geometry, and soliton theory in nonlinear spin systems. Full article

Robust indoor positioning, crucial to modern location-based services, increasingly leverages Channel State Information (CSI) for its superior multipath resolution over the traditional RSSI. However, current CSI-based methods are hampered by three key limitations: susceptibility to skewed, non-Gaussian noise; informational redundancy from multi-AP configurations; and spatial discontinuities arising from Euclidean-based modeling. To address these challenges, we propose a unified framework that synergistically combines three innovations: (1) an adaptive filtering pipeline that uses wavelet decomposition and dynamic Kalman updates to suppress skewed noise; (2) a graph attention network that optimizes AP selection by modeling spatiotemporal correlations; and (3) a hyperbolic covariance model that captures the intrinsic non-Euclidean geometry of signal propagation. Evaluations on experimental data demonstrate that our framework achieves superior positioning accuracy and environmental robustness over state-of-the-art methods. Crucially, the hyperbolic representation enhances resilience to obstructions by preserving the signal manifold’s true structure, thereby advancing the practical deployment of fingerprinting systems. Full article

This work presents a comprehensive mathematical framework for symmetrized neural network operators operating under the paradigm of fractional calculus. By introducing a perturbed hyperbolic tangent activation, we construct a family of localized, symmetric, and positive kernel-like densities, which form the analytical backbone for three classes of multivariate operators: quasi-interpolation, Kantorovich-type, and quadrature-type. A central theoretical contribution is the derivation of the Voronovskaya–Santos–Sales Theorem, which extends classical asymptotic expansions to the fractional domain, providing rigorous error bounds and normalized remainder terms governed by Caputo derivatives. The operators exhibit key properties such as partition of unity, exponential decay, and scaling invariance, which are essential for stable and accurate approximations in high-dimensional settings and systems governed by nonlocal dynamics. The theoretical framework is thoroughly validated through applications in signal processing and fractional fluid dynamics, including the formulation of nonlocal viscous models and fractional Navier–Stokes equations with memory effects. Numerical experiments demonstrate a relative error reduction of up to 92.5% when compared to classical quasi-interpolation operators, with observed convergence rates reaching $\mathcal{O}\left(n^{-1.5}\right)$ under Caputo derivatives, using parameters $\lambda =3.5$, $q=1.8$, and $n=100$. This synergy between neural operator theory, asymptotic analysis, and fractional calculus not only advances the theoretical landscape of function approximation but also provides practical computational tools for addressing complex physical systems characterized by long-range interactions and anomalous diffusion. Full article

In this article, we present the extended simple equations method (SEsM) for finding exact solutions to systems of fractional nonlinear partial differential equations (FNPDEs). The expansions made to the original SEsM algorithm are implemented in several directions: (1) In constructing analytical solutions: exact solutions to FNPDE systems are presented by simple or complex composite functions, including combinations of solutions to two or more different simple equations with distinct independent variables (corresponding to different wave velocities); (2) in selecting appropriate fractional derivatives and appropriate wave transformations: the choice of the type of fractional derivatives for each system of FNPDEs depends on the physical nature of the modeled real process. Based on this choice, the range of applicable wave transformations that are used to reduce FNPDEs to nonlinear ODEs has been expanded. It includes not only various forms of fractional traveling wave transformations but also standard traveling wave transformations. Based on these methodological enhancements, a generalized SEsM algorithm has been developed to derive exact solutions of systems of FNPDEs. This algorithm provides multiple options at each step, enabling the user to select the most appropriate variant depending on the expected wave dynamics in the modeled physical context. Two specific variants of the generalized SEsM algorithm have been applied to obtain exact solutions to two time-fractional shallow-water-like systems. For generating these exact solutions, it is assumed that each system variable in the studied models exhibits multi-wave behavior, which is expressed as a superposition of two waves propagating at different velocities. As a result, numerous novel multi-wave solutions are derived, involving combinations of hyperbolic-like, elliptic-like, and trigonometric-like functions. The obtained analytical solutions can provide valuable qualitative insights into complex wave dynamics in generalized spatio-temporal dynamical systems, with relevance to areas such as ocean current modeling, multiphase fluid dynamics and geophysical fluid modeling. Full article

Our study lies at the intersection of three fields: finite-time thermodynamics, relativity theory, and the theory of hyperbolic conservation laws. Each of these fields has its own requirements and richness, and in order to link them together as effectively as possible, we have simplified each one, reducing it to its fundamental principles. The example chosen concerns the propagation of chemical changes in a very large reactor, as found in geology. We ask ourselves two sets of questions: (1) How do the finiteness of propagation speeds modeled by hyperbolic problems (diffusion is neglected) and the finiteness of the time allocated to transformations interact? (2) How do the finiteness of time and that of resources interact? The similarity in the behavior of the pairs of variables (x, t and resources, resource flows) in Lorentz relativistic transformations allows us to put them on the same level and propose complementary-type relationships between the two classes of finiteness. If times are finite, so are resources, which can be neither zero nor infinite. In hyperbolic problems, a condition is necessary to select solutions with a physical sense among the multiplicity of weak solutions: this is given by the entropy production, which is Lorentz invariant (and not entropy alone). Full article

This review provides a comprehensive overview of the closed-form expressions developed for estimating the soil water retention curve (SWRC) from 1964 to the present. Since the concept of the SWRC was introduced in 1907, numerous closed-form functions have been proposed to describe the relationship between soil matric suction and volumetric water content, each with distinct strengths and limitations. Given the variability in SWRC shapes influenced by soil texture, structure, and organic matter, models in the form of sigmoidal, multi-exponential, lognormal, hyperbolic, and hybrid functions have been designed to fit experimental SWRC data. Based on the number of adjustable parameters, these models are categorized into three main groups: three-, four-, and five-parameter models. They can also be classified as one-, two-, or three-segment functions depending on their structural complexity. A review of the developed models indicates that most are effective in representing the SWRC between the residual and saturated water content range. To capture the full range of the SWRC, hybrid functions have been proposed by combining traditional models. This review presents and discusses these models in chronological order of publication. Full article

Conventional designs of pile foundations for houses on expansive soils adopt conservative approaches by using swelling pressure measured in oedometer tests to compute pile uplift force. However, in practice, piles are often installed in unsaturated soils, where changes in moisture content influence soil behavior. Increasing moisture in expansive soils reduces matric suction, increases soil volume, and induces swelling pressure, all of which affect uplift shear stress. This study investigates the impact of varying degrees of saturation on pile uplift force through a series of laboratory tests on single-pile models. The results of the experimental investigation indicate that uplift force developed along the pile shaft due to the wetting of expansive soils exhibits a hyperbolic trend. A significant portion of the uplift force developed during the early stage of the heaving process. Back-calculation analyses using theoretical equations reveal that the coefficient of uplift, α, and the swelling pressure ratio, β, increases as the initial degree of saturation of soil specimens increases, with a change of less than 10% within the tested range. These findings suggest that constant values of the α and β parameters can be used for pile design in expansive soils, even under unsaturated conditions. Nonetheless, the influence of other factors, such as pile dimensions, pile materials, and soil properties, on the α and β values should be investigated to improve the accuracy of pile design in expansive soil conditions. Full article

To enhance the speed control performance of the permanent magnet synchronous motor (PMSM) servo system, an improved sliding mode control method integrating a torque observer is presented. The current loop uses current feedback decoupling PID control, and the speed loop applies sliding mode control. In comparison to previous work in hybrid SMC using fuzzy logic and torque observers, this p proposes a hyperbolic tangent function in replacement of the signum function to solve the conflict between rapidity and chattering in the traditional exponential reaching law, and fuzzy and segmental self-tuning rules adjust relevant switching terms to reduce chattering and improve the sliding mode arrival process. A load torque observer is designed to enhance the system’s anti-interference ability by compensating the observed load torque to the current loop input. Simulation results show that compared with traditional sliding mode control with a load torque observer (SMC + LO), PID control with a load torque observer (PID + LO), and Active Disturbance Rejection Control (ADRC), the proposed strategy can track the desired speed in 0.032 s, has a dynamic deceleration of 2.7 r/min during sudden load increases, and has a recovery time of 0.011 s, while the others have relatively inferior performance. Finally, the model experiment is carried out, and the results of the experiment are basically consistent with the simulation results. Simulation and experimental results confirm the superiority of the proposed control strategy in improving the system’s comprehensive performance. Full article